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MIP approach for detailed placement Mixed Integer Programming (MIP) approach placement of each window is formulated into an MIP problem: linear objective function & linear constraints; integer variables mature mathematical techniques for solving MIP problems a branch-and-bound tree is built during solution, whose size is dependent on the number of integer variables MIP models for detailed placement the S model, the RQ model, the SCP model the single-cell-placement (SCP) model over 10 times more efficient than the other MIP models

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IBM Version 2 DAC12 Challenges with recent mixed-size circuits DAC12 benchmark circuits n.c. number of cells o.r. occupation rate, the rate that sites are occupied by cells 400 extracted 10-cell windows n.s. average number of sites n.v. average number of integer variables in SCP model;

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Our contribution DAC12 benchmark circuits over 10 times more cells over 2 times more sites in sliding windows over 10 times increase in solution time of each window Incomplete SCP model ignore a portion of integer variables in SCP model great reduction in solution time without much degradation in solution quality MIP-based detailed placer for DAC12 benchmark circuits

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Incomplete SCP Model (contd) Guideline to set skip exact locations in the solution may be non-optimal guarantee different orders of placing cells are still in the solution space skip=1 for compact windows; larger skip for sparse windows with low occupation rate (ocp_rt) and more empty sites

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Two incomplete SCP models Number of variables for cell c in SCP model: v c is close to summation of cell width, the same as in the SCP model of placing the same cells in a compact window SCP_ES model, set skip based on number of empty sites In compact windows, skip =1 In sparse windows with ocp_rt close to 0.0, v c is close to |C|, the same as in the SCP model of placing the same number of uniform-width cells SCP_OR model, set skip based on occupation rate

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MIP approach for detailed placement optimize larger sliding windows to further reduce wirelength Application in recent large-scale benchmark circuits Over 10 times more cells; Lower occupation rate leading to significant increase in the solution time of each window Incomplete SCP model ignore variables to significantly decrease solution time; Despite degradation in solution quality, still effective reduction in wirelength is achieved without perturbance of routability